1.17 Maximum likelihood and MAP
You can derive a loss function instead of memorizing it.
Before:00. Orientation & SetupUnlocks:03. Data Handling & Analysis04. Classical AI — Agents, Search & Knowledge Representation
Maximum likelihood is the recipe that generates most loss functions: write the probability of the data, take the negative log, minimise. Once cross-entropy falls out of a Bernoulli likelihood in front of you, losses stop being arbitrary facts to memorise. MAP adds a prior and lands exactly where regularisation will. It closes the estimation arc because deriving two losses once replaces memorising twenty. The confusion to fix early is likelihood versus probability — same formula, different variable held fixed.
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Likelihood vs. probability
Probability asks how likely data is given a model; likelihood asks how well a model explains data already seen. Swapping the two is a common and consequential confusion.
Introduction to Probability & Statistics (18.05) · CourseMLE for Bernoulli, normal, linear models
Deriving the best-fitting parameters for the standard simple models, which is where loss functions come from rather than being handed down. Doing it once changes how you read every later loss.
Priors, posteriors and MAP estimation
Adding a prior belief and finding the most probable parameters afterwards, which is the smallest step from one estimation philosophy to the other. It also explains certain penalty terms.
Why cross-entropy is just negative log-likelihood
The classification loss used everywhere in deep learning is exactly a negative log-likelihood. Seeing that removes the sense that loss functions are arbitrary choices.
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